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Although it has been confirmed that the Galactic Starfighter expansion will be PvP only, many people have speculated that this is simply a foundation to build on and that PvE content will follow.
However, a TOR podcaster recently attended the New York community cantina event and had a chance to talk with the devs on the subject. You can listen to the comments starting at 42:05, but here is a direct quote:
"I asked him about the possibility that the current, that Galactic Starfighter was designed with PvE in mind. He said no, it was not. That is far far far far far down on the wall of crazy, is PvE Starfighter. He said the biggest problems would be with scripting and 3D AI; things that they dont have in the game they would basically have to write fresh. The good thing about PvE is the good scripting. Getting the ability in at the right time makes it interesting and fun, but not unfair. You know, getting those enrage timers right. Getting like a DOT thrown out at the right time. Stuff that has to be done really well for PvE to work right. And for them to do that in space would be a lot of work. So problems with scripting and AI would be reasons that we wont be seeing PvE Galactic starfighter. So thats upsetting, I'm not happy about that, I wish that we could, but its understandable. And hopefully they make a good system with the Galactic Starfighter."
So while they may change their minds and decide to build on the PvP-only foundation one day, that is not their current plan, and it definitely wont be any time in the foreseeable future.